Questions: Simplify completely, assuming both x>0 and y>0: sqrt(49 x^3 y^5)

Solution Steps

To simplify the given expression \(\sqrt{49 x^{3} y^{5}}\), we can break it down into the product of square roots of its factors. We know that \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\). We can also use the property that \(\sqrt{a^2} = a\) for any non-negative \(a\).

We start with the expression \(\sqrt{49 x^3 y^5}\). We can break this down into the product of square roots of its factors: \[ \sqrt{49 x^3 y^5} = \sqrt{49} \cdot \sqrt{x^3} \cdot \sqrt{y^5} \]

Next, we simplify each square root individually: \[ \sqrt{49} = 7 \] \[ \sqrt{x^3} = x^{3/2} \] \[ \sqrt{y^5} = y^{5/2} \]

We combine the simplified terms to get the final simplified expression: \[ \sqrt{49 x^3 y^5} = 7 \cdot x^{3/2} \cdot y^{5/2} \]

Final Answer